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Yes, you can use Cantor's diagonal argument to enumerate all triples. No, it does not answer the question whether every integer can be written as the sum of thr
by stabbles 7y ago
Yes, you can use Cantor's diagonal argument to enumerate all triples. No, it does not answer the question whether every integer can be written as the sum of three cubes; it only would if the set of integers was finite.
- kmill 7y agoDiagonal argument? (That's how you show something is uncountable.) It's that finite Cartesian products of countable sets are countable https://proofwiki.org/wiki/Cartesian_Product_of_Countable_Sets_is_Countable https://proofwiki.org/wiki/Cartesian_Product_of_Countable_Se...
- stabbles 7y agoOh, that's funny, thanks for pointing that out. I had exactly this in mind (or the proof that the set of rational numbers are countable), but mistakenly thought it was called the 'diagonal argument' because you would get the bijection to the natural numbers by counting diagonally through the table.